A stochastic template placement algorithm for gravitational wave data analysis

This paper presents an algorithm for constructing matched-filter template banks in an arbitrary parameter space. The method places templates at random, then removes those which are "too close" together. The properties and optimality of stochastic template banks generated in this manner are investigated for some simple models. The effectiveness of these template banks for gravitational wave searches for binary inspiral waveforms is also examined. The properties of a stochastic template bank are then compared to the deterministically placed template banks that are currently used in gravitational wave data analysis.Comment: 14 pages, 11 figure

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitationalwave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44 Msun. The choice of the lower frequency cut off is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.Comment: 18 pages, 11 figures, Matches with the published versio

Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems

We apply the recent results of F. Hiai, M. Mosonyi and T. Ogawa [arXiv:0707.2020, to appear in J. Math. Phys.] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasi-free states on a CAR algebra. We use a multivariate extension of Szego's theorem to show the existence of the mean Chernoff and Hoeffding bounds and the mean relative entropy, and show that these quantities arise as the optimal error exponents in suitable settings.Comment: Results extended to higher dimensional lattices, title changed. Submitted versio

Genital Chronic Graft-versus-Host Disease in Females: A Cross-Sectional Study

AbstractUsing the National Institutes of Health (NIH) consensus criteria for chronic graft-versus-host disease (cGVHD), we assessed the prevalence, symptoms, and clinical signs of female genital cGVHD in a cross-sectional population-based study. Forty-two women were evaluated at a median of 80 months (range, 13 to 148 months) after undergoing hematopoietic stem cell transplantation (HSCT). Medical history, ongoing medications, and genital signs and symptoms were recorded. Gynecologic examination for the diagnosis and clinical scoring of genital cGVHD was combined with clinical scoring of extragenital cGVHD for the estimation of each patient's global cGVHD score. Biopsy specimens from the genital mucosa were obtained from 38 patients. Genital cGVHD was diagnosed in 22 of 42 patients (52%). Its presence was associated with systemic corticoid steroid treatment of extragenital cGVHD (P = .001), older age (P = .07), and HSCT from a sibling donor (P = .002). Five patients had isolated genital cGVHD. Dryness, pain, smarting pain (P < .05 for all), and dyspareunia (P = .001) were observed more frequently in the women with genital cGVHD. Twelve patients had advanced genital cGVHD (clinical score 3), which was the main factor explaining the high rate (15 of 42) of severe global cGVHD. The rate of genital cGVHD was similar (P = .37) in patients with a follow-up of ≥80 months (10 of 22) and those with a follow-up of <80 months (12 of 20). We found no convincing relationship between clinical diagnosis and histopathological assessment of mucosal biopsy specimens. In our group of women with a long follow-up after HSCT, genital cGVHD was common and in many cases incorrectly diagnosed. Genital cGVHD causes genital symptoms and affects sexual life, and may present without any other cGVHD, warranting early and continuous gynecologic surveillance in all women after HSCT

Gravitational Wave Chirp Search: Economization of PN Matched Filter Bank via Cardinal Interpolation

The final inspiral phase in the evolution of a compact binary consisting of black holes and/or neutron stars is among the most probable events that a network of ground-based interferometric gravitational wave detectors is likely to observe. Gravitational radiation emitted during this phase will have to be dug out of noise by matched-filtering (correlating) the detector output with a bank of several $10^5$ templates, making the computational resources required quite demanding, though not formidable. We propose an interpolation method for evaluating the correlation between template waveforms and the detector output and show that the method is effective in substantially reducing the number of templates required. Indeed, the number of templates needed could be a factor $\sim 4$ smaller than required by the usual approach, when the minimal overlap between the template bank and an arbitrary signal (the so-called {\it minimal match}) is 0.97. The method is amenable to easy implementation, and the various detector projects might benefit by adopting it to reduce the computational costs of inspiraling neutron star and black hole binary search.Comment: scheduled for publicatin on Phys. Rev. D 6

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.

Applications of distance between probability distributions to gravitational wave data analysis

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the proper distance defined using the Fisher matrix as a metric on the parameter space. We consider using our notion of distance in several problems in gravitational wave data analysis: to place templates in the parameter space in searches for gravitational-wave signals, to assess quality of search templates, and to study the signal resolution.Comment: 18 pages, 5 figure

Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesised that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(\sigma_1,...,\sigma_r), as recently introduced by Nussbaum and Szko{\l}a in analogy with Salikhov's classical multi-hypothesis Chernoff bound. This quantity is defined as the minimum of the pairwise binary Chernoff divergences min_{j<k}C(\sigma_j,\sigma_k). It was known already that the optimal asymptotic rate must lie between C/3 and C, and that for certain classes of sets of states the bound is actually achieved. It was known to be achieved, in particular, when the state pair that is closest together in Chernoff divergence is more than 6 times closer than the next closest pair. Our results improve on this in two ways. Firstly, we show that the optimal asymptotic rate must lie between C/2 and C. Secondly, we show that the Chernoff bound is already achieved when the closest state pair is more than 2 times closer than the next closest pair. We also show that the Chernoff bound is achieved when at least $r-2$ of the states are pure, improving on a previous result by Nussbaum and Szko{\l}a. Finally, we indicate a number of potential pathways along which a proof (or disproof) may eventually be found that the multi-hypothesis quantum Chernoff bound is always achieved.Comment: 50 pages. v3: Slightly restructured, main results unchanged, connection to Barnum and Knill's result (arXiv:quant-ph/0004088) clarified. Accepted for JM